DECOMPOSITION FORMULAE FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE GAUSS-KUMMER IDENTITY

Title & Authors
DECOMPOSITION FORMULAE FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE GAUSS-KUMMER IDENTITY
Hayashi, Naoya; Matsui, Yutaka;

Abstract
In the theory of special functions, it is important to study some formulae describing hypergeometric functions with other hypergeometric functions. In this paper, we give some methods to obtain a lot of decomposition formulae for generalized hypergeometric functions.
Keywords
generalized hypergeometric functions;Gauss-Kummer identity;decomposition formulae;
Language
English
Cited by
1.
Generalized hypergeometric function identities at argument±1, Integral Transforms and Special Functions, 2014, 25, 11, 909
References
1.
J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math. Oxford Ser. 11 (1940), 249-270.

2.
J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric function. II, Quart. J. Math. Oxford Ser. 12 (1941), 112-128.

3.
T. W. Chaundy, Expansions of hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942), 159-171.

4.
J. Choi and A. Hasanov, Applications of the operator H(${\alpha}$, ${\beta}$) to the Humbert double hypergeometric functions, Comput. Math. Appl. 61 (2011), no. 3, 663-671.

5.
J. Choi and A. Hasanov, Certain decomposition formulas of generalized hypergeometric functions $_pF_q$ and some formulas of an analytic continuation of the Clausen function $_3F_2$, Commun. Korean Math. Soc. 27 (2012), no. 1, 107-116.

6.
A. Hasanov and H. M. Srivastava, Some decomposition formulas associated with the Lauricella function $F_A^{({\gamma})}$ and other multiple hypergeometric functions, Appl. Math. Lett. 19 (2006), no. 2, 113-121.

7.
A. Hasanov and H. M. Srivastava, Decomposition formulas associated with the Lauricella multivariable hypergeometric functions, Compt. Math. Appl. 53 (2007), no. 7, 1119-1128.

8.
A. Hasanov, H. M. Srivastava, and M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl. 324 (2006), no. 2, 955-969.

9.
A. Hasanov, M. Turaev, and J. Choi, Decomposition formulas for the generalized hypergeometric $_4F_3$ function, Honam Math. J. 32 (2010), no. 1, 1-16.

10.
K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida, From Gauss to Painleve, A modern theory of special functions, Aspects of Mathematics, E16, Friedr. Vieveg & Sohn, Braunschweig, 1991.

11.
H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted press, Wiley, New York, 1985.